Vacuum Chamber Setup

The vacuum chamber setup employed in these studies is shown in figure 2.6 and consists of a pair of differentially pumped chambers, termed the source and interaction chambers. Within the source chamber is housed the molecular beam source, an Even-Lavie (E-L) pulsed solenoid valve,[7] and this chamber is pumped by a turbo pump (Oerlikon Leybold Mag W 2200) which maintains a pressure of <5 × 10-6 mbar when the valve is operating. The interaction chamber is separated from the source chamber by a 2 mm skimmer that samples the centre of the molecular beam. Within the interaction chamber are the electrostatic lens electrodes that form the velocity map imaging (VMI) setup.[8] CaF2 windows on either side of the

chamber allow for alignment of the laser beams into the interaction chamber, intersecting the molecular beam in the centre of the electrostatic lens setup. The interaction chamber is pumped by a turbo pump (Oerlikon Leybold Turbovac Mag W 700), maintaining a pressure of <2 × 10-7 mbar when the valve is operating. Both turbo pumps are backed by a two-stage rotary pump (Oerlikon Leybold Trivac D 40- B), which maintains a backing pressure of <2 × 10-2 mbar.

Mounted vertically above the interaction chamber is a time of flight (TOF) tube at the terminus of which is the VMI detector, which lies approximately 500 mm away from the centre of the electrostatic lens. The TOF and detector setup can be employed to either provide VMI data or, by measuring the arrival time of a particular ion, it can also be employed as a basic mass spectrometer. Further details on VMI arrangement will be discussed (in section 2.2.2).

Figure 2.6 – Schematic of the vacuum chamber setup. The chamber to the left is the source chamber containing the pulsed solenoid valve; the chamber to the right is the interactions chamber containing the electrostatic lens setup and VMI detector.

2.2.1 Molecular Beams

The desire to study the energetics of isolated molecular systems typically requires that the molecules have a well-defined internal energy. Often in spectroscopy the aim is to carry out studies on molecules starting in low vibrational and rotational eigenstates. As the population of vibrational and rotational levels will be governed by a Boltzmann factor ( P∝e−∆E K T) it is clear that low internal temperatures are required to ensure population of the lowest vibrational and

beams in which the molecule of interest (analyte) is discharged in a beam of seed gas through a nozzle into a vacuum, a schematic of which is shown in figure 2.7.

Figure 2.7 – Schematic of the pulsed solenoid valve, representation of the region of supersonic beam created and how skimming the centre of the distribution yields a molecular beam “packet” with high translational energy (Etrans) and a low internal energy (Eint).

If the pressure difference on either side of the nozzle is large enough, supersonic beam velocities can be achieved. Upon entering vacuum, the beam undergoes an expansion that transfers the internal energy of the molecules (Eint) to the translational

energy (Etrans) of the seed gas through inelastic collisions. This transfer of energy

ensures the low vibrational and rotational temperatures required for spectroscopy, particularly if the translationally quickest molecules are studied. By introducing a skimmer that removes the subsonic sections of the molecular beam, it is possible to sample the coldest segment of the beam which possesses a narrow range of beam velocities. The physics behind molecular beam generation is quite extensive and will not be discussed here, however they are comprehensively reviewed in reference [9].

The use of molecular beams has proven useful in many areas of spectroscopy, however using a continuous beam can cause problems as the large volume of gas necessitates large vacuum pumps in order to maintain high vacuum, and large

samples of analyte which can be costly. One solution to this problem is to use a pulsed valve that is synchronised with the means of detection, allowing for the study of small “packets” of molecular beam without the large through-put of gas. Furthermore the use of a pulsed system allows for detection of the front edge of a molecular beam “packet” which will have the highest translational velocity and therefore lowest internal temperature. The experiments herein implement a pulsed solenoid valve (Even-Lavie) operating at 125 Hz (N.B. synchronising with 1 in 8 laser pulses), the design of which allows for high seed gas pressures and controlled analyte heating. Previous studies with the Even-Lavie valve have suggested rotational temperature as low as <1 K can be achieved.[7] The valve works by retracting a spring-loaded magnetic plunger with a solenoid-induced magnetic field. The plunger is then returned by the spring mechanism once the field is removed.

The choice of seed gas for a molecular beam greatly affects the beam velocity and composition. In all the experiments herein a helium seed gas was used, which gives a beam velocity of ~1780 ms-1 which is obtained by using equation 2.5 [10, 11]: 2 B 1 5 k 2m v = 2 Tva lv e (2.5)

where m is the atomic mass of the seed gas, v is the beam velocity, kB is the

Boltzmann constant and Tvalve is the temperature of the pulsed-valve. The use of

argon as a seed gas was considered in the studies presented, however due to the much slower beam velocities achieved a larger number of molecular clusters were formed. The opening of the valve was triggered relative to the laser pulses by the

the valve opening time so that the front edge of the molecular beam arrives in the interaction region at the same time as the laser pulses. For more details on timing see below.

Typical Operating Conditions

For each molecule studied the temperature and the opening time of the pulsed valve was optimised to produce a sufficient amount of sample in the molecular beam. A summary of typical operating conditions for all the molecules studied in this thesis are shown in table 2.2, along with the melting and boiling point for each molecule.

Table 2.2 – Summary of typical operating conditions for the molecules studied, including literature melting points and boiling points.

Molecule Melting Point / °C Boiling Point / °C Operating Temperature / °C Valve Opening Time / µµµµs Imidazole 90 256 100 13.5 4 – Methylimidazole 142 267 140 12.5 2 – Methylimidazole 45 263 150 13.5 2,4 – Dimethylimidazole 86 266 100 14.5 1 – Methylimidazole -6 198 100 15 Anisole -37 154 80 14 Mequinol 55 243 120 14 Thioanisole -15 188 80 12

All chemicals were above 98 % purity and purchased from Sigma-Aldrich. Solid samples were inserted as powders into the Even-Lavie valve sample tube between the seed gas inlet and solenoid valve mechanism (See figure 2.7). For the liquid samples, 1 – Methylimidazole, Anisole and Thioanisole, a sample was absorbed onto a piece of filter paper and inserted into the sample tube.

2.2.2 Velocity Map Imaging

As discussed earlier the desire to measure the kinetic energy of photofragments can be achieved through several techniques. For the work in this thesis VMI is employed as this allows for the detection of a photofragment’s kinetic energy and angular distribution. Furthermore VMI can be employed to study fragments of varying mass (which is not always possible with high Rydberg time of flight techniques, as discussed in section 1.3.2). Imaging of photoproducts was first performed by Chandler and Houston [12] during the 1980s using a gridded set of Wiley-McLaren type electrodes. However, it was the development of the electrostatic lens setup by Eppink and Parker [8] that allowed for velocity mapping, yielding a significant improvement in kinetic energy resolution.

The VMI setup utilised in this thesis is schematically shown in figure 2.8. The electrostatic lens is shown on the left and consists of two electrodes, termed the repeller and extractor, which are based on a pair of grid-less Wiley-McLaren TOF electrodes. Furthermore, a ground electrode is included further down the flight tube to shield against stray electric fields (similar to a Wiley-McLaren setup [13]). The typical operating voltages applied to the repeller (Vr) and extractor (Ve) are 5000 and

microchannel plates (MCP), which serve to amplify the ion signal through a cascade of electron impacts, and a phosphor P-43 (Gd2O2S:Tb) screen which luminesces

upon electron impact. The luminescence is then capture by a charge couple device (CCD) array (Basler A-312-f) and recorded by a purpose built LabVIEW program. Typical operating voltages for the MCP vary from 600 to 800 V behind the first MCP (Vmcp1) and from 1200 to 1600 V behind the second MCP (Vmcp2). The voltage

on Vmcp2 is kept at double that of Vmcp1 ensuring a consistent gain over both MCP

plates. The P-43 screen is maintained at 5 kV.

Figure 2.8 – Schematic of the velocity map imaging setup including the electrostatic lens electrodes (left); the field free flight path and deflector (middle); and the detector consisting of two MCPs, P-43 screen and CCD array. The laser pulses (hν) have an electric field polarised in the Z-axis. Projection of the ions is vertically in the laboratory frame (Y-axis).

The VMI setup is situated within the interaction chamber so that the propagating molecular beam (in the Z-axis in figure 2.8) and laser beam (propagating in the X-axis – with an electric field polarised along the Z-axis) intersect in the middle of the electrostatic lens. The electrostatic lens projects the Newton sphere of charged particles along the Y-axis. The Wiley-McLaren type electrode setup causes

the ion Newton sphere to become temporally compressed while in flight, leading to a “pancaking” of ions as they impact upon the detector (see figure 2.8).

Velocity Mapping

The equations governing the projection of charged particles along a TOF setup were originally provided by Wiley-McLaren. These state that for an optimised setup (Ve/Vr) an ion of specific m/z will be temporally focused onto the position

sensitive detector, at the end of a TOF tube length L (L≈ 500 mm), independently of

the initial position within the molecule-laser interaction region. The TOF (ttof) for a

particular fragment is given by:

t of

m

t L

2eVr

≈ (2.6)

where m is the mass of the fragment and e is the elementary charge on an electron.

For the electrostatic lens used in VMI the velocity of the photofragment within the Newton sphere will be mapped onto a specific position on the detector. The radius of the “pancaked” Newton sphere of an ion upon impact is given by:

xz t of

KER

r av t aL

eVr

≈ ≈ (2.7)

The radius is therefore dependent on ttof, the ion’s velocity perpendicular to the flight

axis (vxz) and a magnification factor (a). From this it can be shown that the kinetic

energy release (KER) of an ion can be related to r2. This latter relationship is key for extracting a TKER spectrum from the 2D distribution and calibration of the VMI setup (see below). a is characteristic of the velocity mapping conditions and typically

2.7 is that the mapping of an ion’s velocity is independent of the ion’s position within the molecule-laser interaction region. This significantly improves the KER

resolution of the experiment as it overcomes the limits imposed by the size of the laser focus or the Doppler broadening from the molecular beam’s motion. The independence from the ion’s initial position is nicely illustrated in figure 2.9, taken from the original Eppink and Parker paper,[8] which shows Simion-calculated trajectories for the same ion at different initial positions within the electrostatic lens for an electrode setup with a voltage ratio Ve/Vr = 0.75.

Figure 2.9 – Simulated ion trajectories for ions in an electrostatic lens field (shown as equipotential lines) with the same kinetic energy ejected at three different angles relative to the direction of flight. b-d) show zoomed-in sections of the trajectories. Reprinted with permission from reference [8]. The Need for Image Reconstruction

The mapping of ions from a three dimensional (3D) distribution of ions on a Newton sphere to a 2D image can be described, with reference to figure 2.10, by the conversion from a 3D polar distribution, F(r,

θ

,

φ

), where

θ

and

φ

are the zenith and

azimuthal angles and r is the radius of the sphere, to a 2D projection G(R,

α

) where

α

is the angle and R is the radius of the circle. The projection of the Newton sphere of

ions causes a reduction of dimensionality. As a result the contribution from signal with a non-zero azimuthal angle (

φ

≠ 0) will become convoluted into the 2D

distribution G(R,

α

) at a reduced R from

φ

= 0 signal (and imposing upon signal with

a lower 3D radius (r)).

Figure 2.10 – Velocity mapping of a 3D Newton sphere distribution of charged particles with velocity (v), which can be described in polar coordinate as the function F(r,θ,φ). The distribution is required to be cylindrically symmetric around the Cartesian Z-axis. This distribution is then projected along the Y-axis and mapped as a 2D distribution in terms of a radius (R) and an angle (α) from the Cartesian Z-axis.

The angles

θ

and

α

are defined relative to the polarisation of the laser’s electric field

(Z-axis in figure 2.10) that lies perpendicular to the VMI projection axis (Y-axis in figure 2.10). A laser polarisation perpendicular to the VMI projection axis is essential otherwise distinction of the

θ

and

φ

contribution to the convoluted 2D

distribution is not possible.

As implied by equation 2.7 a one dimensional radial spectrum is proportional to KER, therefore determining the ion signal intensity as a function of r can yield a spectrum of the photofragments KER. The intensity of the 1D radial distribution I(r)

is given by:

2π π

0 0

( )

( , , )

I r

=

∫ ∫F r

θ φ θ φd d

(2.8) Obtaining the distribution F(r,

θ

,

φ

) from its projection G(R,

α

) is therefore essential to

determining I(r) and from it a KER spectrum. Attaining F(r,

θ

,

φ

) from G(R,

α

) can be

achieved through image deconvolution, which involves a series of transformations. A schematic of the basic steps are shown in figure 2.11.

Figure 2.11 – Schematic of the steps involved in image deconvolution. From a 2D image, an effective slice at φ = 0 is taken and the 3D distribution determined. This is then converted to a 1D radial spectrum by integration over all angles.

The first stage in deconvolution is to account for the reduction in dimensionality and remove the contribution from signal with

φ

≠ 0 in the initial

Newton sphere, yielding F(

θ

,r,

φ

= 0). This can be achieved through one of numerous mathematical algorithms.[14-17] The work in this thesis uses a polar onion peeling (POP) algorithm developed by Roberts et al.[18] Once the effective slice through the

signal at

φ

= 0 is determined the distribution of the initial Newton sphere, F(r,

θ

,

φ

),

can be recovered. Finally, by employing equation 2.8 it is possible to convert

F(r,

θ

,

φ

) to a 1D radial spectrum, which can yield a KER spectrum through

conversion with a known calibration factor. The calibration factor is derived from analysis of a system with a known dissociation energy (hydrogen bromide and methyl iodide – see calibration section 2.4.2).

Photoproduct Angular Dependence

The angular distribution of photoproducts relative to the electric field vector of the light (defined in the Z-axis in figures 2.8 and 2.10) can be indicative of the nature of the electronic states accessed upon photoexcitation. Photofragment angular distributions arise due to the directionality of the transition dipole moment (TDM) of the pump transition, which was discussed earlier in relation to equation 1.5 for a case where unpolarised light is used. Within the Franck-Condon principle it can be shown that the probability of an electronic transition induced by polarised light is proportional to the electric field vector by:

P∝

∫

ψe′(µ εe )ψe′′dτ (2.9) where εεεε is the electric field vector of the polarised light, µµµµe is the electronic dipole

wavefunctions for the ground and excited electronic state, respectively. As µµµµe and εεεε are vectors, transitions will preferentially occur in molecules when the two vectors are parallel to each other. Typically it is easy to consider the alignment of εεεε and the

observable, the TDM (where T D M=

∫ψ

_e′′µ_e

ψ

_e′d

τ

2) for the transition. In a gaseous sample, this alignment leads to the formation of a set of molecules in an excited electronic state that are aligned in a particular direction relative to the laser polarisation, which is polarised along the Z-axis (see figure 2.8) of the laboratory frame. If the excited electronic state results in dissociation, this alignment is maintained in the distribution of photoproducts, with the photofragment’s position dependent on the angle between the TDM (for the transition) and the dissociating bond.

Figure 2.12 – A schematic of the 2D VMI images resulting from the photodissociation of a diatomic molecule whose transition dipole moment (TDM) is aligned a) parallel and b) perpendicular to the dissociating bond. The VMI images are representations of the image before deconvolution, in terms of

α; but correspond to a 3D distribution where the maximum signal is located at a) θ = 0° and b) θ = 90°.

The angular distribution that results from a one-photon excitation has a cosine-squared dependence on the angle between the electric field vector of the laser pulse and the TDM. Due to this, the two limiting cases of ion distribution can be described by a c o s2θ _{distribution for a system where the TDM is parallel to the}

dissociating bond and s i n2θ distribution when the TDM in perpendicular to the dissociating bond. The VMI images arising from these two limiting cases are shown in figure 2.12, where 2.12 a) is the parallel and 2.12 b) the perpendicular case.[14]

Typically for larger molecules the distribution of photofragments does not fit a limiting case. This occurs when: i) the absorption to two electronic states takes place; ii) the TDM lies at an angle between 0° and 90° to the dissociating bond; or iii) when the rotational period of the molecule is on a comparable timescale to the dissociation. To obtain a quantitative measure of how the photofragments are angularly distributed, the intensity of photofragments (I(

θ

)) is fit to the lowest even

term of the Legendre polynomial (P2(x)) for a cosine distribution:

2 2 2 2 1 1 1 I( ) [1 P ( c o s ) ] [1 (3c o s 1) ] 4π 4π 2 θ = +β θ = +β θ − (2.10)

where

β

2 is the anisotropy parameter for a one-photon dissociation process and

quantifies the angular distribution.

β

2 can take values between -1 and 2, where -1

corresponds to a photofragment distribution perpendicular to εεεε and 2 corresponds to a photofragment distribution parallel to εεεε. A

β

2 value of zero refers to an isotropic

distribution which can arise from one of three possible situations: 1) a dissociation occurring far slower than the rotational period of the molecule; 2) excitation to a set of closely lying electronic states whose TDM combine to give an isotropic

distribution; or 3) a TDM that lies at 54.7° (“magic” angle) with respect to the dissociating bond.[14, 18-20]

It is important to note that the value of

β

2 describes the distribution I(

θ

)

relative to the εεεε of the polarised light. However, from this the angular relationship between the TDM and the dissociating bond can be inferred. The TDM can be derived from first principles (symmetry arguments) or calculated by various computational techniques. By comparing the calculated TDM to I(

θ

) it is possible to

distinguish the excited state that is accessed prior to dissociation.[14, 18] It is also important to note that higher order evens terms of the Legendre polynomial and

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